It’s a big trip covering half the country so a bit open ended.
In Yellowstone we stayed at the rv park in fishing bridge. Packed in like sardines but avoiding driving in and out of the park every day was completely worth it. Yellowstone is easily worth a week if you do any hiking or outdoor activities. It’s big, driving distances are long, varied topography.
Grand Teton we stayed in Colter Bay. Good location. GTNP is worth half a week unless you are into alpine touring or climbing. It’s much smaller than YNP.
Glacier is spectacular. Weather can be quite unpredictable, I’ve gotten snow there in August on the continental divide and had to end a backpacking trip early. Another trip I got eaten alive by mosquitoes. Another trip I got hypothermia in a sleet storm. In fact I have yet to spend any time in Glacier and not have terrible weather. I would spend a week in Glacier, but I’m a hiker. Note that the eastern entrance is closed this year because the Blackfeet reservation is closed to visitors. Maybe that’s not an issue next year, but with that entrance closed you can’t access some spectacular sites like the Many Glacier area. I’ve never RV camped in this area, but anything near Many Glacier would be my choice.
In S Dak we really enjoyed the Badlands. Surprisingly interesting hiking. We saw a ton of sheep there. Camping options are limited, the KOA White River is a little old, pool was closed, golf is really run down, but it’s quiet and shaded. IN contrast the campground in the national park is baking in the sun. I’d pick the KOA and I don’t like KOAs.
Custer SP is amazing. Definitely worth several days. Mt Rushmore was open. The two caves (Wind Cave and Jewel Cave) were closed but the hiking was open. Deadwood was boring, We liked Keystone better.
Devil’s Tower is cool and worth a day.
We really liked Little BIghorn and were disappointed not to be able to see the Wounded Knee site (all Indian reservations are closed to the public).
Depending on your route, There is a ton to see in Colorado. RMNP is gorgeous, worth several days. The San Juan skyway scenic drive is very pretty, not sure taking a large rig on it is ideal but I think it’s doable. Much gorgeous scenery in the national forests, etc. Tons of mosquitoes in early summer. Bring headnets and potentially bug jackets.
Coming home through eastern Utah and Western Colorado you can stop at Flaming Gorge, Dinosaur NM, Arches, Canyonlands, Black Canyon of the Gunnison, and Mesa Verde and Durango CO. All of them are amazing, especially Arches and Canyonlands.
In both Glacier and Yellowstone you absolutely need bear spray if you do any hiking at all.